Lecture 26

Learning objectives

After this class, you should be able to:

1. Given a hash function, the hash table size, and a sequence of insertions and deletions, draw the state of open-addressed (if a collision resolution strategy too is given) or chained hash tables after the operations are complete.
2. Derive the worst case and expected case time complexities for hash table insertion, search, and deletion.

Reading assignment

1. Section 10.2.2 (excluding coalesced hashing), 10.2.3 (excluding the strategy demonstrated in fig. 10.10d), class notes.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Show the state of an open-addressed hash table of size 23 with p(i) = i + 3 after the following sequence of operations are complete. Also give the number of hash table entries searched for each of the following operations. Use the function f1 defined in class, for the hashing. insert("abcd"), insert("dbcd"), search("decd"), insert("abdc"), insert("bbcd"), insert("dabc"), insert("decd"), delete("abdc"), search("dabc"), search("abdc").
  2. Show the state of an chained-addressed hash table of size 23 after the following sequence of operations are complete. Also give the number of hash table entries searched for each of the following operations. Use the function f1 defined in class, for the hashing. insert("abcd"), insert("dbcd"), search("decd"), insert("abdc"), insert("bbcd"), insert("dabc"), insert("decd"), delete("abdc"), search("dabc"), search("abdc").
  3. Let an open addressed hash table be resized by doubling whenever n/T exceeds 0.5. Show that the amortized time complexity for n insertions is O(n).

• Questions on next lecture's material
  1. None.